Finite Group Databasebeta

← Group #264251

Character table — Group #264251

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-111111-1-11-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ1722222222222-2-2-2-220000-2-22222-2-2-2-200002222000000000000000000-200-200000000
χ1822222222222-2-2-2-220000-2-22222-2-2-2-20000-2-2-2-2000000000000000000200200000000
χ1922222222222-2-2-2-220000-2-2-2-2-2-22222000022-2-2000000000000000000-200200000000
χ2022222222222-2-2-2-220000-2-2-2-2-2-222220000-2-222000000000000000000200-200000000
χ2122222222-2-2-22222-22222-2-20000000022-2-20000-2-222-2-2000000000000000000000000
χ2222222222-2-2-22222-22222-2-200000000-2-2220000-2-2-2-222000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-20000000022-2-2000022-2-222000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-200000000-2-22200002222-2-2000000000000000000000000
χ2522-22-22-2-20002-22-2022-2-200i2i2−i2−i2i2i2−i2−i2002i−2i000000002i−2ii2i2−i2−i222−2−222−2−2000000000000
χ2622-22-22-2-20002-22-2022-2-200i2i2−i2−i2i2i2−i2−i200−2i2i00000000−2i2ii2i2−i2−i2−2−222−2−222000000000000
χ2722-22-22-2-20002-22-2022-2-200−i2−i2i2i2−i2−i2i2i2002i−2i000000002i−2i−i2−i2i2i2−2−222−2−222000000000000
χ2822-22-22-2-20002-22-2022-2-200−i2−i2i2i2−i2−i2i2i200−2i2i00000000−2i2i−i2−i2i2i222−2−222−2−2000000000000
χ2922-22-22-2-20002-22-20-2-22200i2i2−i2−i2i2i2−i2−i2002i−2i00000000−2i2i−i2−i2i2i222−2−2−2−222000000000000
χ3022-22-22-2-20002-22-20-2-22200i2i2−i2−i2i2i2−i2−i200−2i2i000000002i−2i−i2−i2i2i2−2−22222−2−2000000000000
χ3122-22-22-2-20002-22-20-2-22200−i2−i2i2i2−i2−i2i2i2002i−2i00000000−2i2ii2i2−i2−i2−2−22222−2−2000000000000
χ3222-22-22-2-20002-22-20-2-22200−i2−i2i2i2−i2−i2i2i200−2i2i000000002i−2ii2i2−i2−i222−2−2−2−222000000000000
χ332-22-222-2-20002-2-2202-22-200i2−i2i2−i2i2−i2i2−i22-2000000002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ342-22-222-2-20002-2-2202-22-200i2−i2i2−i2i2−i2i2−i2-2200000000-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ352-22-222-2-20002-2-2202-22-200−i2i2−i2i2−i2i2−i2i22-2000000002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ362-22-222-2-20002-2-2202-22-200−i2i2−i2i2−i2i2−i2i2-2200000000-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ372-22-222-2-20002-2-220-22-2200i2−i2i2−i2i2−i2i2−i22-200000000-2200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ382-22-222-2-20002-2-220-22-2200i2−i2i2−i2i2−i2i2−i2-22000000002-200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ392-22-222-2-20002-2-220-22-2200−i2i2−i2i2−i2i2−i2i22-200000000-2200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ402-22-222-2-20002-2-220-22-2200−i2i2−i2i2−i2i2−i2i2-22000000002-200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ412-2-2-2-222222-222-2-2-22-2-222-200000000000000002-2000000002i−2i−2i2i2i−2i−2i2i000000000000
χ422-2-2-2-222222-222-2-2-22-2-222-200000000000000002-200000000−2i2i2i−2i−2i2i2i−2i000000000000
χ432-2-2-2-222222-222-2-2-2-222-22-20000000000000000-22000000002i−2i−2i2i−2i2i2i−2i000000000000
χ442-2-2-2-222222-222-2-2-2-222-22-20000000000000000-2200000000−2i2i2i−2i2i−2i−2i2i000000000000
χ452-2-2-2-2222-2-2222-2-222-2-22-222-2-222-2-2200000000-2200002-2-2200000000000000000000
χ462-2-2-2-2222-2-2222-2-222-2-22-22-222-2-222-200000000-220000-222-200000000000000000000
χ472-2-2-2-2222-2-2222-2-22-222-2-222-2-222-2-22000000002-20000-222-200000000000000000000
χ482-2-2-2-2222-2-2222-2-22-222-2-22-222-2-222-2000000002-200002-2-2200000000000000000000
χ492-2-2-2-2222-2-22-2-222200002-22-2-22-222-20000000000000000000000000002-202-2000000
χ502-2-2-2-2222-2-22-2-222200002-22-2-22-222-2000000000000000000000000000-220-22000000
χ512-2-2-2-2222-2-22-2-222200002-2-222-22-2-220000000000000000000000000002-20-22000000
χ522-2-2-2-2222-2-22-2-222200002-2-222-22-2-22000000000000000000000000000-2202-2000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-4-44-44-440000-4000000000000000000000000000000000000000000000022−220000
χ55444-4-4-44-44-440000-40000000000000000000000000000000000000000000000−22220000
χ56444-4-4-44-4-44-4000040000000000000000004i−4i00000000000000000000000000000000
χ57444-4-4-44-4-44-400004000000000000000000−4i4i00000000000000000000000000000000
χ5844-44-44-4-4000-44-4400000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-44-44-4-4000-44-440000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-44-444-4-4000-444-400000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-44-444-4-4000-444-40000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-4-444-44-44-4-400004000000000000000000004-4000000000000000000000000000000
χ634-4-444-44-44-4-40000400000000000000000000-44000000000000000000000000000000
χ644-4-444-44-4-4440000-40000000000000000000000000000000000000000000000002i2−2i200
χ654-4-444-44-4-4440000-4000000000000000000000000000000000000000000000000−2i22i200
χ664-4-4-4-444444-4-4-444-40000-440000000000000000000000000000000000000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-8-8-88000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).